Table 19.

Thresholds’ FPR item level - non-invariance scenario

				FPR item level - thresholds
				MG-CCFA				MG-IRT
				Comb		χ 2		LoR		LRT
N	C	J	%	small	large	small	large	small	large	small	large
250	3	5	20%	0.044	0.058	0.049	0.058	0.131	0.269	0.056	0.054
			40%	0.063	0.045	0.063	0.046	0.149	0.310	0.040	0.036
			40% ±	0.056	0.068	0.058	0.068	0.136	0.312	0.053	0.048
		25	20%	0	0	0.046	0.051	0.005	0.028	0.044	0.048
			40%	0	0	0.050	0.048	0.006	0.031	0.051	0.046
			40% ±	0	0	0.047	0.045	0.006	0.031	0.046	0.049
	5	5	20%	0.041	0.063	0.041	0.063	0.029	0.160	0.043	0.057
			40%	0.055	0.045	0.055	0.052	0.045	0.209	0.048	0.064
			40% ±	0.045	0.047	0.045	0.050	0.039	0.191	0.046	0.046
		25	20%	0	0	0.047	0.053	0	0.017	0.052	0.044
			40%	0	0	0.051	0.050	0.001	0.019	0.051	0.047
			40% ±	0	0	0.046	0.053	0	0.018	0.047	0.051
1000	3	5	20%	0.023	0.027	0.053	0.069	0.007	0.163	0.040	0.058
			40%	0.018	0.010	0.058	0.056	0.012	0.257	0.045	0.060
			40% ±	0.022	0.024	0.061	0.096	0.008	0.248	0.047	0.057
		25	20%	0	0	0.051	0.052	0	0.001	0.048	0.053
			40%	0	0	0.046	0.054	0	0	0.047	0.051
			40% ±	0	0	0.053	0.051	0	0.001	0.050	0.048
	5	5	20%	0.022	0.012	0.059	0.072	0	0.087	0.052	0.048
			40%	0.012	0.004	0.048	0.062	0	0.117	0.053	0.045
			40% ±	0.015	0.006	0.060	0.114	0	0.128	0.041	0.050
		25	20%	0	0	0.051	0.047	0	0	0.047	0.041
			40%	0	0	0.054	0.053	0	0	0.050	0.051
			40% ±	0	0	0.048	0.047	0	0	0.048	0.046

The bold entries were used to distinguish between design factors and do not refer to results

Note. MG-CCFA = Multiple-group categorical confirmatory factor analysis; MG-IRT LoR = Logistic regression with MG-IRT; MG-IRT LRT = Likelihood-ratio test with MG-IRT; N = Sample size within each group; C = Number of categories; J = Number of items; % = percentage of items affected by DIF (± misaligned); small = small bias; large = large bias